A uniform rod of length $L$ lies on a smooth horizontal table. The rod has a mass $M .$ A particle of mass $m$ moving with speed $v$ strikes the rod perpendicularly at one of the ends of the rod sticks to it after collision.
Find the velocity of the centre of mass $C$ and the angular, velocity of the system about the centre of mass after the collision.

(2 m v), (M + m), \frac{3 M v}{( M + 2 m ) L}

(M v), (M + m), \frac{6 M v}{( M + 4 m ) L}

(2 m v), (M + m), \frac{3 M v}{( M + 4 m ) L}

(m v), (M + m), \frac{6 M v}{( M + 4 m ) L}

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William Discussed

A uniform rod of length

L

lies on a smooth horizontal table. The rod has a mass

M .

A particle of mass

m

moving with speed

v

strikes the rod perpendicularly at one of the ends of the rod sticks to it after collision.
Find the velocity of the centre of mass

C

and the angular, velocity of the system about the centre of mass after the collision.

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